Mathematics and Art: Mathematical Visualization in Art and EducationClaude Bruter Recent progress in research, teaching and communication has arisen from the use of new tools in visualization. To be fruitful, visualization needs precision and beauty. This book is a source of mathematical illustrations by mathematicians as well as artists. It offers examples in many basic mathematical fields including polyhedra theory, group theory, solving polynomial equations, dynamical systems and differential topology. For a long time, arts, architecture, music and painting have been the source of new developments in mathematics. And vice versa, artists have often found new techniques, themes and inspiration within mathematics. Here, while mathematicians provide mathematical tools for the analysis of musical creations, the contributions from sculptors emphasize the role of mathematics in their work. |
Contents
Presentation of the Colloquium The ARPAM Project | 1 |
SolidSegment Sculptures | 14 |
Visualizing Mathematics Online | 25 |
The Design of 2Colour Wallpaper Patterns Using Methods Based on Chaotic Dynamics and Symmetry | 39 |
Machines for Building Symmetry | 57 |
The Mathematics of Tuning Musical Instruments a Simple Toolkit for Experiments | 75 |
The Garden of Eden | 85 |
Visualization and Dynamical Systems | 87 |
Presentation of the Atractor | 156 |
Forum Discussion | 162 |
Forum Discussion | 164 |
Getting Out of the Box and Into the Sphere | 169 |
Constructing Wire Models | 175 |
from Smale through The Optiverse | 197 |
Tactile Mathematics | 209 |
Hyperseeing Knots and Minimal Surfaces | 219 |
Mathematical Aspects in the Second Viennese School of Music | 101 |
The Film Series | 115 |
Guided Tours of Buried Galleries Inside a Computer | 131 |
A Mathematical Interpretation of Expressive Intonation | 137 |
Symbolic Sculptures | 145 |
How Art Can Help the Teaching of Mathematics? | 149 |
Forum Discussion | 151 |
Ruled Sculptures | 229 |
A Gallery of Algebraic Surfaces | 233 |
The Mathematical Exploratorium | 263 |
Copper Engravings | 269 |
Color Plates | 271 |
Index | 331 |
Other editions - View all
Mathematics and Art: Mathematical Visualization in Art and Education Claude P. Bruter Limited preview - 2013 |
Mathematics and Art: Mathematical Visualization in Art and Education Claude P. Bruter No preview available - 2010 |
Common terms and phrases
abstract algebraic surface algorithms Apéry art and mathematics artists attractor basic beautiful catenoid Cayley cubic colours construct corresponding Coxeter Coxeter groups create cube cubic surface curvature curve defined Dick Termes double points dynamics Emmer equation Escher example exhibition Exploratorium fact fifth Figure finite function G-symmetric Gallery gastrulation geometry graphics halfway-model Hessian hexachord hyperseeing idea inside integration interactive interesting iteration Java JavaView lines M.C. Escher Math mathematical visualization mathematicians meridians minimal surface mirror box Möbius band Morin musical objects octave pattern of type permutations planar plane Plate PlayScale Polthier polyhedra polyhedron polynomial possible problem quartic rotation scale Science sculpture segments singular soap films space sphere eversion Steiner surface structure subgroup symmetry group three-dimensional tone torus knot triangle tuning two-colour pattern vertices wallpaper group wallpaper patterns wire